Analogous results arise from considering a fully classical damped harmonic oscillator with complex position \(r_c(t)\) , driven by the force \(f_c(t)=\sqrt{\Delta }\exp [-(\Delta /2 + i\omega _L) t]\) , with a slowly-varying amplitude \(\Delta \ll \Gamma \) , where \(\Gamma \)  is the oscillator dissipation rate.
We then have from Newtonian dynamics that \(r_c(t) \approx \chi _c f_c(t)\) , so the classical work reads
\(W_{\mathrm {cl}}\equiv \int _0^\infty 2\Re [f_c^* \partial _t r_c]dt= - \int _0^\infty 2\Re [r_c^* \partial _t f_c]dt\approx \Delta \chi _c^{\prime } + 2\omega _L \chi _c^{\prime \prime }\) ,
where \(\Delta \chi _c^{\prime }\)  is the reactive (dispersive) part, and \(2\omega _L \chi _c^{\prime \prime }\)  is the absorptive part (see ref.[1]}).
